Hemififths: Difference between revisions

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== Notation ==

Hemififths can be notated in [[neutral circle-of-fifths notation]], in which case 5/4 is represented by a sesqui-augmented second (C-D#+), and 7/4 by a semi-augmented sixth (C-A+). In the 13-limit extension, 11/8 is represented by the semi-augmented fourth (C-F+), and 13/8 by the neutral sixth (C-Ad). This, of course, defies the tradition of tertian harmony. The just major triad on C is C-D~~#+-~~G, for example. One may want to adopt an additional module of accidentals such as arrows to represent the comma step. There are two solutions:

Hemififths can be notated in [[neutral circle-of-fifths notation]], in which case 5/4 is represented by a sesqui-augmented second (C-D{{sesquisharp2}}), and 7/4 by a semi-augmented sixth (C-A{{demisharp2}}). In the 13-limit extension, 11/8 is represented by the semi-augmented fourth (C-F{{demisharp2}}), and 13/8 by the neutral sixth (C-A{{demiflat2}}). This, of course, defies the tradition of tertian harmony. The just major triad on C is {{dash|C, D{{sesquisharp2}}, G|med}}, for example. One may want to adopt an additional module of accidentals such as arrows to represent the comma step. There are two solutions:

# let an arrow represent a bend by the syntonic~septimal comma (17 gensteps, semidiminished second);

# let an arrow represent a bend by the Pythagorean comma (24 gensteps, negative diminished second).

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Below is tabulated how to notate the prime harmonics with an arrow representing a syntonic~septimal comma.

{| class="wikitable center-1 center-3"

|+Hemififths nomenclature<br>for selected intervals

|+ style="font-size: 105%;" | Hemififths nomenclature<br />for selected intervals

|-

! Ratio

! Nominal

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Below is tabulated how to notate the prime harmonics with an arrow representing a Pythagorean comma.

{| class="wikitable center-1 center-3"

|+Hemififths nomenclature<br>for selected intervals

|+ style="font-size: 105%;" | Hemififths nomenclature<br />for selected intervals

|-

! Ratio

! Nominal

@@ Line 168: / Line 168: @@
 == Notation ==
-Hemififths can be notated in [[neutral circle-of-fifths notation]], in which case 5/4 is represented by a sesqui-augmented second (C-D#+), and 7/4 by a semi-augmented sixth (C-A+). In the 13-limit extension, 11/8 is represented by the semi-augmented fourth (C-F+), and 13/8 by the neutral sixth (C-Ad). This, of course, defies the tradition of tertian harmony. The just major triad on C is C-D#+-G, for example. One may want to adopt an additional module of accidentals such as arrows to represent the comma step. There are two solutions:
+Hemififths can be notated in [[neutral circle-of-fifths notation]], in which case 5/4 is represented by a sesqui-augmented second (C-D{{sesquisharp2}}), and 7/4 by a semi-augmented sixth (C-A{{demisharp2}}). In the 13-limit extension, 11/8 is represented by the semi-augmented fourth (C-F{{demisharp2}}), and 13/8 by the neutral sixth (C-A{{demiflat2}}). This, of course, defies the tradition of tertian harmony. The just major triad on C is {{dash|C, D{{sesquisharp2}}, G|med}}, for example. One may want to adopt an additional module of accidentals such as arrows to represent the comma step. There are two solutions:
 # let an arrow represent a bend by the syntonic~septimal comma (17 gensteps, semidiminished second);
 # let an arrow represent a bend by the Pythagorean comma (24 gensteps, negative diminished second).
@@ Line 174: / Line 174: @@
 Below is tabulated how to notate the prime harmonics with an arrow representing a syntonic~septimal comma.
 {| class="wikitable center-1 center-3"
-|+Hemififths nomenclature<br>for selected intervals
+|+ style="font-size: 105%;" | Hemififths nomenclature<br />for selected intervals
+|-
 ! Ratio
 ! Nominal
@@ Line 202: / Line 203: @@
 Below is tabulated how to notate the prime harmonics with an arrow representing a Pythagorean comma.
 {| class="wikitable center-1 center-3"
-|+Hemififths nomenclature<br>for selected intervals
+|+ style="font-size: 105%;" | Hemififths nomenclature<br />for selected intervals
+|-
 ! Ratio
 ! Nominal